Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
Quantum Physics
2022-08-31 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We discuss the exceptional Laguerre and the exceptional Jacobi orthogonal polynomials in the framework of the supersymmetric quantum mechanics (SUSYQM). We express the differential equations for the Jacobi and the Laguerre exceptional orthogonal polynomials (EOP) as the eigenvalue equations and make an analogy with the time independent Schr\"odinger equation to define "Hamiltonians" enables us to study the EOPs in the framework of the SUSYQM and to realize the underlying shape invariance associated with such systems. We show that the underlying shape invariance symmetry is responsible for the solubility of the differential equations associated with these polynomials.
Keywords
Cite
@article{arxiv.2206.03902,
title = {Supersymmetry and Shape Invariance of exceptional orthogonal polynomials},
author = {Satish Yadav and Avinash Khare and Bhabani Prasad Mandal},
journal= {arXiv preprint arXiv:2206.03902},
year = {2022}
}
Comments
Latex, 16 Pages